Test of Companies’ Action after Restatements:

provision-specific variables in model (1) and re-run the analysis. Based on our economic bond notion, restricted stocks and long-term options shall further reinforce the importance of equity-based compensation to AC members’ wealth, leading to a higher restatement likelihood. Therefore, hypothesis H3-1 predicts more significant coefficients for RESTRSTOCK and LONGOPTION than for UNRESTRSTOCK and SHORTOPTION.

Under the percentage approach, variables CASH%_AC, STOCK%_AC, and OPTION%_AC are the ratios of cash, stocks, and options to total compensation, respectively. We thus replace CASH_AC, STOCK_AC, and OPTION_AC by these three percentage variables in model (1). According to hypotheses H4-1 and H4-2, we predict the coefficients of STOCK%_AC and OPTION%_AC to be positive and the coefficient of CASH%_AC to be negative.

Finally, we test the economic bond effects using the ratios of restricted and unrestricted stocks (denoted by RESTRSTOCK% and UNRESTRSTOCK%, respectively) and short-term and long-term options (denoted by SHORTOPTION% and LONGOPTION%, respectively) to total compensation. We replace STOCK%_AC and OPTION%_AC by these four provision-specific percentage variables in model (1). Hypothesis H3-2 thus predicts that the coefficients of RESTRSTOCK% and LONGOPTION% are more significant than those of UNRESTRSTOCK% and SHORTOPTION%.

3.3 Test of Companies’ Action after Restatements:

To test our hypotheses H5 ~ H9, we use the differences-in-differences method following Bertrand et al. (2004), Bertrand and Mullainathan (1999, 2003), and Low (2009). Specifically, we adopt the following regression model:

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where the definitions of all the variables are summarized in the Appendix.

The dependent variables are chosen depending on the hypotheses to be tested. For example, we use CASH_AC and EQUITY_AC as the dependent variables to test our H5 and H6, respectively. To examine whether restating companies’ adjustments in equity compensation is specifically due to ACs and whether such adjustments are the consequence of the decline in CEOs' equity-based compensation following restatements (Cheng and Farber 2008), we also employ compensation paid to the CEOs and board members other than ACs and CEOs as the dependent variables for comparison purpose. Under the magnitude approach, we define CASH_CEO and CASH_OthB to be the natural logs of cash compensation paid to the CEOs and other board members, respectively. In addition, we measure EQUITY_CEO and EQUITY_OthB by the natural logs of equity-based compensation paid to the CEOs and other board members, respectively.

Under the percentage approach, we use CASH%_AC and EQUITY%_AC to test H8 and H9, respectively. Similar to the tests of H5 and H6, we use the portions of compensation paid to the CEOs and other board members as the dependent variables to supplement our tests of H8 and H9. We define CASH%_CEO and CASH%_OthB to be the ratios of CEOs’ and other board members’ cash compensation to total compensation, respectively. Also, EQUITY%_CEO and EQUITY%_OthB are measured by the ratios of equity-based compensation to total compensation for the CEOs and other board members, respectively.

Based on the extent of economic bond tying up AC members’ wealth and companies’ financials, we further decompose EQUITY_AC into two groups: a strong economic bond group (including restricted stocks and long-term options) and a weak economic bond group (including unrestricted stocks and short-term options). To test hypothesis H7-1, we use S_BOND (which is the natural log of the sum of restricted stocks and long-term options) and W_BOND (which is the natural log of the sum of unrestricted stocks and short-term options) as our dependent variables. To test hypothesis H7-2, we

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use S_BOND% (which is the ratio of restricted stocks and long-term options to total compensation) and W_BOND% (which is the ratio of unrestricted stocks and short-term options to total compensation) as our dependent variables.

Due to a lack of literature that investigates the determinants of ACs’ cash and equity-based compensation when restatements occur, we follow Engel et al. (2010) and Linck et al. (2009) by including several control variables that may affect board director compensation. For example, Linck et al. (2009) indicates that, according to the contracting theory (Jensen and Murphy 1990), directors’

compensation is affected by their job complexity (which can be measured by firm size), financing activities, and firm performance. We use LnASSET and SALES to proxy for firm size (Chhaochharia and Grinstein 2009; Engel et al. 2010) and adopt LEVERAGE and ROA_ind to capture financing activities and performance (Engel et al. 2010; Linck et al. 2009), respectively. Since the changes in compensation could be related to systematic difference in changes to firms’ growth opportunities (Chhaochharia and Grinstein 2009), we use the market-to book ratio (denoted by M/B) to control for this effect (Engel et al. 2010; Ryan and Wiggins 2004).

Based on the bargaining theory (Bebchuk et al. 2002; Hermalin and Weisbach 1998), Engel et al.

(2010) indicates that directors’ compensation is determined by the negotiation process between the boards and the CEOs. To measure boards’ negotiation power, Engel et al. (2010) suggests the use of the percentage of independent directors on the boards (denoted by IndBOARD). To measure CEOs’

bargaining power, Engel et al. (2010) suggests the use of CEO ownership (denoted by CEOOWN%) and whether CEOs serve as chairs of the boards (denoted by CHAIRCEO). We further consider the number of directors (denoted by BSIZE) because Ryan and Wiggins (2004) indicates that board size also affect CEOs’ bargaining power. Moreover, Engel et al. (2009) shows that companies are more likely to structure their AC compensation when their demand for monitoring (measured by total audit fees, denoted by AUDITFEE) changes. We follow Engel et al. (2010) by including this variable in

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model (2). Finally, we capture companies’ cash constraints in paying cash compensation by including variable DIVIDENDS in the model (Engel et al. 2010; Linck 2009).

Since there is a lack of prior studies and theories that can possibly explain the relations between our dependent and independent variables, we predict no signs for our control variables in model (2).

The differences-in-differences estimator represents the difference between the pre-post, within-subjects differences of the treatment and control groups (Ashenfelter, 1978; Bertrand et al.

2004). ANREST is a dummy variable that equals 1 if a company announces a restatement in a given year and 0 otherwise. This variable tests whether there are significant differences in the dependent variables between companies with and without restatements. POST is a dummy variable that equals 1 if the year is after the year of restatement announcement and 0 otherwise. Here we use restatement announcement years instead of years being restated because companies adjust ACs’ compensation only after restatements are publicly announced.

Our variable of interest, ANRESTPOST, tests whether there are significant changes in dependent variables before and after restatements. When we use CASH_AC and CASH%_AC as the dependent variables to test hypotheses H5 and H8, respectively, we expect the coefficients of ANRESTPOST to be positive because companies will pay more cash or higher portion of cash to their ACs due to increased demanding for monitoring resulting from restatements. In contrast, when we use EQUITY_AC and EQUITY%_AC as the dependent variables to test hypotheses H6 and H9, respectively, we expect the coefficients of ANRESTPOST to be negative because companies perceive that equity-based compensation jeopardizes AC independence and decide to reduce such payments to improve ACs’ oversight quality. Lastly, hypotheses H7-1 and H7-2 predict that companies will reduce more amounts and portions of stocks and options that create stronger economic bond to the ACs.

Therefore, we expect the coefficients of ANRESTPOST to be larger when we use S_BOND and S_BOND% as the dependent variables than when we use W_BOND and W_BOND% as the dependent

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variables, respectively. Similar to Model (1), we also control for industry and year fixed effects in model (2) for potential unspecified factors.

4. EMPIRICAL RESULTS